The electric field (as a vector) at a distance z along the z-axis
[tex]E = \frac{1}{4 \pi ε0} \frac{ 2 \pi r dr }{1} \frac{1}{\sqrt{a^{2} + z^{2} } } -\frac{1}{b^{2} + z^{2} }[/tex]
We take a small circular element on the ring with the radius 'dr' , It is given that the ring is uniformly charged with charge density ∝
so the total charge in the small ring with thickness dr is
[tex]d_{q}[/tex] = [tex]2[/tex] [tex]\pi[/tex] [tex]r \ d_{r}[/tex]
We know that the electric field at point 'z ' units away on the line passing through the centre of the ring is
[tex]E = \frac{1}{4 \pi ε0} \frac{ 2 \pi r dr }{\sqrt[\frac{3}{2} ]{ r^{2} + z^{2} } }[/tex]
The inner radius is ' a' The outer radius is 'b'
Integrating the above equation from a to b
[tex]E = \frac{1}{4 \pi ε0} \frac{ 2 \pi r dr }{1} \frac{1}{\sqrt{a^{2} + z^{2} } } -\frac{1}{b^{2} + z^{2} }[/tex]
If limit 'a' goes to zero
[tex]E = \frac{1}{4 \pi ε0} \frac{ 2 \pi r dr }{1} ( \frac{1}{ } -\frac{1}{b^{2} + z^{2} })[/tex]
Using Binomial expansion and ignoring terms of higher power
[tex]E = \frac{1}{4 \pi ε0} \pi ∝ b^{2}[/tex]
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A Ferris wheel has radius 46 meters and it moves at a rate of 2 revolutions per minute. Approximate the angular velocity of the Ferris wheel ω in radians per minute. Give approximation correct to one decimal place.
The angular velocity of the Ferris wheel can be calculated using the formula ω = (2π/60) × (2 rev/min), where 2π radians is equal to 360 degrees.
What is the radians ?Radians are a unit of measure used in mathematics and trigonometry to measure angles. It is defined as the angle subtended at the center of a circle by an arc of the circumference that is equal in length to the radius of the circle. Radians are used to measure angles in both two-dimensional and three-dimensional space, and can be expressed as a ratio of the length of the arc to the radius of the circle. The most common radian measure is the radian, which is equal to 180/π degrees.
ω ≈ 0.4 rad/min
The angular velocity of the Ferris wheel can be calculated using the formula ω = (2π/60) × (2 rev/min), where 2π radians is equal to 360 degrees.
Therefore, ω = (2π/60) × (2 rev/min) = (2π/30) rad/min ≈ 0.4 rad/min.
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pull the balloon back to about the midpoint between the wall and the sweater. release it again and describe the motion of the balloon using kinematics concepts of velocity and acceleration.
In summation, the balloon's motion may be defined as an entity undergoing steady downward acceleration, with a starting velocity of zero and rising velocity as time passes.
Describe the motion of the balloon using kinematics concepts of velocity and acceleration.The motion of the balloon may be characterized using kinematic principles of velocity and acceleration when it is pushed back to the halfway between the wall and the sweater and then released. The balloon has an initial velocity of zero, v0 = 0, at the instant of release. The gravitational force pressing on it causes it to accelerate downwards. The balloon's acceleration may be described as the acceleration owing to gravity, a = 9.8 m/s2. As time passes, the balloon's velocity rises due to its acceleration. The balloon's velocity may be calculated using the equation v = v0 + at, where t denotes time. The balloon's location may be characterized by the equation x = x0 + v0t + (1/2)at2, where x0 represents the balloon's original position. The balloon's velocity will grow during its travel, reaching its maximum value at the instant it hits its lowest point. Because the balloon is only being affected upon by the constant force of gravity, its acceleration will remain constant.
Here,
In summary, the motion of the balloon can be described as an object undergoing constant acceleration in the downward direction, with an initial velocity of zero and increasing velocity as time progresses.
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An elevator is moving upward and speeding up. What is the sign of the work done by the force of gravity acting on the elevator? A) positive B) Negative C) Zero D) this question cannot be answered without knowing the direction of the elevator's acceleration.
The downward force caused by gravity will be the same as the normal force, that is the power of the elevators on this child's shoes. So, 98 newtons will be the typical force in this situation.
What does force in physics mean?
You can also use words like stretch and compress to describe force. Force is described in physics as the pull or push that causes a massed object to change its speed. Force is an outside agent that has the power to alter a body's resting or moving position.
What is a good instance of force?
When applied, force is an outside factor that modifies or tends to modifies a body's condition; if indeed the body is moving
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which of the following statements accurately represents the relationship between linear and angular motion? none of the answers are correct. linear motion of joints produces an angular motion. angular motion of joints produces the linear motion of walking, and linear motion of joints produces an angular motion. angular motion of joints produces the linear motion of walking.
The correct statement is: Angular motion of joints produces the linear motion of walking.
Angular motion is the motion of a body about a fixed point or fixed axis. It is equal to the angle passed over at the point or axis by a line drawn to the body.Relationship between linear and angular motion are as follows:Displacement – In linear motion, we use ‘s’ to quantify the linear distance travelled. In angular motion, we use ‘θ’ for the same to quantify the angular distance, and it is measured in radians.
Velocity – In linear motion, we use ‘v’ to denote velocity while in angular motion, we use ‘ω’ to indicate angular velocity. Angular velocity is the number of radians covered per second.
Acceleration – We use ‘a’ to denote linear acceleration, while we use ‘α’ to mean angular acceleration. The unit of angular acceleration is radians per second square
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how many degrees are there on both the celsius and kelvin temperature scales, between the normal freezing and boiling points of water?
On both the the celsius and kelvin temperature scales, 100 degrees is the difference between normal freezing and boiling points of water.
Boiling point
The temperature at which a fluid bubbles and goes to fume for example significantly alters its state at climatic strain is known as the edge of boiling over of the fluid.
Bubbling is a mass peculiarity.Edge of boiling over of waterThe edge of boiling over of water is the edge of boiling over of water fluctuates with air pressure.We know that on celsius scale,freezing temperature of water is =0°C
and,boiling point of water is =100°C
Similarly,freezing point of water in kelvin scale=273K
and boiling point of water in kelvin scale=373K.
So,difference between normal freezing point of water and boiling point of water=100-0=100°C
Hence,difference is of 100°C in both kelvin and degree scale.
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Determine the required concentration (in percent by mass) for an aqueous ethylene glycol (C2H6O2) solution to have a boiling point of 108.3 ∘C. Express your answer using two significant figures. nothing % %
The required concentration (in percent by mass) for an aqueous ethylene glycol (C2H6O2) solution is 51 %.
What is Ethylene glycol?A helpful industrial substance called ethylene glycol can be found in a variety of consumer goods. Antifreeze, some stamp pad inks, ballpoint pens, solvents, paints, plastics, films, and cosmetics are a few examples. It may also serve as a delivery system for drugs.
Because of its pleasant flavor, ethanol is frequently consumed intentionally or by mistake. In the body, ethylene glycol decomposes into harmful substances.
The central nervous system (CNS), followed by the heart and kidneys, are the first organs that are impacted by ethylene glycol and its harmful byproducts.
Therefore, The required concentration (in percent by mass) for an aqueous ethylene glycol (C2H6O2) solution is 51 %.
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a bicyclist moving at a speed of 15.0 m/s rounds a bend with a radius of 28.0 m. what is the centripetal acceleration of the cyclist?
Centripetal acceleration of the cyclist is 8.04 m/s^2, while the moving speed of the cyclist is 15.0m/s.
The centripetal acceleration of an object moving in a circle with a radius "r" and velocity "v" can be calculated using the following formula:
a = v^2 / r
where "a" is the centripetal acceleration.
Given the speed of the cyclist
(v) = 15.0 m/s and
the radius of the bend (r) = 28.0 m,
the centripetal acceleration can be calculated as follows:
= a
= v^2 / r
= (15.0 m/s)^2 / 28.0 m
= 225 m^2/s^2 / 28 m
= 8.04 m/s^2
So the centripetal acceleration of the cyclist is 8.04 m/s^2.
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what is the time for one cycle of the radio wave?
A radio wave's frequency is the number of cycles it completes in one second, and is measured in hertz (Hz).
One cycle of a radio wave is the time it takes for the wave to complete a cycle of its waveform, from the peak to the trough, and back to the peak again. A radio wave's frequency is the number of cycles it completes in one second, and is measured in hertz (Hz). For example, a radio wave with a frequency of 1 MHz (one million hertz) will have a cycle time of 1 microsecond (one millionth of a second).
The cycle time of a radio wave is the inverse of its frequency, and represents the time it takes for the wave to complete one full cycle of its waveform, from peak to trough and back to peak again. The higher the frequency, the shorter the cycle time, and vice versa.
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A box weighing 43.2 N is pulled horizontally until it slides uniformly over a
level floor. If the applied force is 6.30 N, what is the coefficient of
friction between the box and the floor?
The coefficient of friction between the box and the floor is approximately 0.852.
What do you mean by force?Force is a concept in physics that refers to a push or pull upon an object that results in a change in the object's motion. Forces can cause objects to accelerate, change direction, or change shape. In physics, a force is a vector quantity, meaning it has both magnitude and direction.
Forces can be caused by many factors, including gravity, electromagnetic fields, and the interaction between objects. They can be measured in units of Newtons (N), and the effects of forces can be described by Newton's laws of motion, which explain how objects will respond to different forces.
The coefficient of friction (μ) can be calculated using the formula:
μ = Friction force / Normal force
where the friction force is equal to the applied force minus the force due to gravity on the box:
Friction force = Applied force - Force due to gravity
The force due to gravity on the box is given by:
Force due to gravity = weight of box = 43.2 N
So, substituting these values, we get:
μ = (Applied force - 43.2 N) / 43.2 N
μ = (6.30 N - 43.2 N) / 43.2 N
μ = -36.9 N / 43.2 N
μ = -0.852
Since the coefficient of friction can only be positive, the negative sign indicates that the direction of the friction force is opposite to that of the applied force.
Therefore, the coefficient of friction between the box and the floor is approximately 0.852.
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which of jupiter's moons was found to have active volcanoes on it?
The stony moon of Jupiter With hundreds of eruptions, some of which are spouting lava fountains that are a few kilometers (or kilometers) high, Io is the solar system's largest volcanically active planet.
What makes Jupiter so distinctive?By far the biggest world in the solar system, Jupiter is more than times as large than all of the other planet put altogether. Jupiter is the sixth planet from our Sun. The swirls and patterns of Jupiter are really urea and water clouds floating in a helium- and hydrogen-rich atmosphere.
Jupiter has to be either hot or cool.The clouds tops are thought to be roughly -280 degrees Fahrenheit frigid. The overall temperature of Mars is -238 degrees Fahrenheit. Jupiter's pole is only little more than 3 degrees inclined, therefore
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i need help on this please answer rrght away!
f the coefficient of static friction between the axe and the wood is ms = 0.2, determine the smallest angle u of the blade which will cause the axe to be self-locking. neglect the weight of the axe.
The smallest angle u of the blade which will cause the axe to be self-locking is θ=22.6 degree
EFy=0
2(N sin θ/2)-2(0.2N cos θ/2)=0
tan theta/2= 0.2
θ= 22.6 degree
The frame, locking hydraulic cylinder, and cam self-locking mechanism make up the self-locking system, which makes sure that the robot's traction is greater than the locking force. The locking cam, two guide wheels, a guide plate, and a connecting rod are the basic components of the cam self-locking mechanism.
We have done so succinctly and plainly. Lead screw nuts and lead screws that are self-locking cannot be moved without the use of external force. The pitch and coefficient of friction are relevant. In many instances, self-locking enables the user to do without an expensive brake.
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what is the particle's angular velocity at a) t =1
At time t = 1 s, the particle's angular velocity is 6.28 rad/s (role="math" localid="1652184311109").
w = theta / t, where w = angular velocity, theta = position angle, and t = time, denotes the rate of change of an object's position angle with respect to time. Therefore, the wheel's angular velocity at t=15s t = 15 s is 8.33rad/s 8.33 r a d/s. A particle's instantaneous velocity, or v(t), is the derivative of its position relative to time. Therefore, v(t)=dxdt. This derivative is frequently represented by the symbols x(t) or just x. The amount of rotational angle (or angular displacement) made by a rotating body in one unit of time is known as its angular velocity.Omega () is used to represent it. Angular velocity is defined mathematically as rad/s = dtd. SI units are measured in radians per second.
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what is the magnitude of a vertical electric field that will just barely counterbalance the weight of a plastic bead of mass 2.20 g if the bead has been charged to 1.40 μc?
The required magnitude of a vertical electric field that will just barely counterbalance the weight of a plastic bead is calculated to be 15.42 × 10³ C.
The mass of the bead is given as, m = 2.2 g = 2.2 × 10⁻³ kg
The charge on the bead q = 1.4 μc = 1.4 × 10⁻⁶ c
Magnitude of vertical electric field = ?
The electric field's force on the charged plastic sphere equals q E.
The plastic spherical is m g in weight.
where, g is the acceleration due to gravity
Now the force due to electrostatic field is balanced by the weight of the plastic sphere.
q E = m g
E = m g / q
E = (2.2 × 10⁻³)(9.81)/(1.4 × 10⁻⁶) = (2.2 × 9.81 × 10³)/1.4 = 15.42 × 10³ C
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what's the mass of the Sun?
Volume and mass The sun has a total volume of 1.4 x 10 28 cubic meters. According to NASA data, 1.3 million Earths might fit inside the sun.
How does physics define mass?
It is the most fundamental characteristic of matter and one of the basic quantities in physics. Mass is a term used to describe how much matter is there in a body. The kilogram is the SI mass unit. (kg). A body's mass does not alter at any point in time. only in rare instances where a significant quantity of energy is supplied to or taken away from a body.
How is mass determined?
Mass can be calculated using the formula: mass = volume density. Weight serves as a gauge for gravitational force.
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activation-synthesis theory- dreams are caused by random neural firings combined with memories
manifest conent- literal content of a dream
freuds theory of dreams- dreams can be used to access unconscious conflicts
non-rem dreams- mundane, dull, everyday events when asleep
rem dreams- illogical, bizarre, and highly visual experiences when asleep
latent content- what a dream symbolizes
The Activation-Synthesis Theory is a neurobiological way to explain the origin of dreams.
A neurobiological theory that explains the neurogenesis of dreams is called the Activation-Synthesis Theory. According to the activation-synthesis dream theory, also known as the neural activation theory, when people dream, their minds are attempting to make sense of the brain activity occurring in the brain stem. The study of nervous system cells and the function of the signals that pass through the nervous system is known as neurobiology. The brain is still quite active while dreaming. The body's biochemical and survival processes are still being carried out by the brain, which is also recharging the body for the next day. These physiological functions of survival include breathing, blood circulation, and healing. The brain stem, often known as the lower half of the brain, carries out these functions.
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what is the maximum pressure (gauge) of the pressurized gas that the pipe can carry before the mercury spills out of the open end of the manometer
The maximum pressure that a pipe can carry before the mercury spills out of an open-end manometer depends on the height of the mercury column and the density of the gas.
An open-end manometer is a device used to measure fluid pressure, usually in a gas or liquid. It consists of a U-shaped tube filled with a liquid, typically mercury or water, and has one end open to the atmosphere.
The pressure of the fluid being measured is transferred to the liquid in the manometer, which results in a change in the height of the liquid column. This change in height can then be used to calculate the pressure, based on the density of the liquid and the height of the column.
The pressure can be calculated using the equation of hydrostatic pressure: Pressure = (density of mercury * acceleration due to gravity * height of mercury column).
The maximum pressure is reached when the pressure exerted by the gas in the pipe equals the pressure exerted by the mercury column, which results in the mercury spilling out of the open end of the manometer.
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A string is stretched between two clamps held 4.02 m apart. The string is made to oscillate at its third harmonic frequency.
Calculate the distance in m between two adjacent nodes to.
The distance between two adjacent nodes of the wave is determined as 8.04 m.
What is the distance between two adjacent node?
The distance between two adjacent nodes of the wave is calculated by applying the following formula;
Node to Node = λ/2
Node to Node = length of the string = 4.02 m
where;
λ is the wavelength of the wave or the distance between two adjacent nodesThe distance between two adjacent nodes of the wave is calculated as;
λ/2 = L
λ = 2L
λ = ( 2 ) x ( 4.02 m )
λ = 8.04 m
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a particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. find the velocity and speed when t = 9.
The value of velocity at t = 9 when the equation of motion is given is calculated to be -1.0123.
The given function is f(t) = (t^-1) - t, it is an equation of motion.
On derivation of the equation of motion, we get the equation of velocity.
Taking derivative on both the sides of the function,
f'(t) = d/dt[(t^-1) - t)] = d/dt(t^-1) - d/dt(t)
f'(t) = -1(t^-2) -1
f'(t) = -t^-2 - 1
f'(t) = v(t),
It can be also written as,
-1/t^2 - 1
To find out the velocity at t = 9, place the value in the above equation.
So, v(9) = -1/(9^2) - 1 = -1/81 - 1 = -0.0123-1 = -1.0123
The given question is incomplete. The complete question contains 'f(t) = (t ^-1) - t.'
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does the skateboarder and the energy appear to be similar to what we saw in the previous two labs? how?
This can only be determined based on the specific labs conducted in the previous two experiments and the information provided about the current situation.
The similarity between the skateboarder and the energy observed in the previous two labs can only be determined based on the specific information and observations made during those experiments. Without any specific details about the previous two labs, it is impossible to make a comparison between the skateboarder and the energy in the current situation.
To make a comparison, we need to know the specific variables that were being studied in the previous two labs and the specific observations made. For example, if the previous two labs were studying the conservation of energy and the relationship between kinetic and potential energy, then a comparison could be made by observing the skateboarder's kinetic energy, potential energy, and total energy as he moves along the ramp.
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a student must conduct an experiment in which an elastic collision occurs. in the experiment, block x of mass 2kg travels with a velocity vx in the positive direction toward block y of mass 2kg that is at rest, as shown in figure 1. after the collision, block y travels in the positive direction with velocity vy while block x remains nearly at rest. data collected of the initial and final velocities of both blocks for three trials of the experiment are shown in the table. did the student conduct an experiment in which an elastic collision occurred? is the system of block x and block y open or closed?
Yes, the student conducted an experiment in which an elastic collision occurred. The system of block x and block y is a closed system.
What is closed system?
A closed system is a system where the components are isolated from the environment. This type of system does not allow any kind of exchange of energy, matter, or information with the environment.
This means that the system is in a state of equilibrium, where the total energy and matter is conserved, and the system is not affected by any external influences.
Therefore, Yes, the student conducted an experiment in which an elastic collision occurred. The system of block x and block y is a closed system.
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an object of mass 1 kg that is moving in a straight line on a level surface slows down from 4 m/s to rest. what is the net work done on the object?
Net work done on the object -16J.
Net work done on the object = Force x Distance
Force = mass x acceleration = 1 kg x (-4 m/s) = -4 N
Distance = Change in velocity x time = (4 m/s - 0 m/s) x 1 s = 4 m
Net work done on the object = Force x Distance
= -4 N x 4 m
= -16 J
What is work done?
Work done is the amount of energy expended to move an object a certain distance. It is calculated by multiplying the force applied to the object by the distance it is moved. Work is measured in Joules (J).
Therefore, Net work done on the object -16J.
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a 65- kg person is skiing down a hill. the skier’s speed at the bottom is 15 m/s. if the skier hits a snowdrift and stops in 0.30 s, (a) how far does she go into the drift? (b) with whay average force will she strike the drift?
If the skier hits a snowdrift and stops in 0.30 s, She would go into the drift to 2.25 m. The average force that she will strike the drift is 3250 N.
What is speed?The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined.
a = -15 / 0.3 = -50 m/s2
v2 - v02 = 2ax
- 152(-50)x == > x = 2.25 m
F = ma = 65 x 50 = 3250 N
Therefore, a. She would go into the drift to 2.25 m.
b. The average force that she will strike the drift is 3250 N.
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Three identical container P, Q and R are taken, and kept - one on the terrace of a tall building; another on the terrace of a horter building; and the third in an open pace. After a rain, which one will have the highet level of water, auming no overflow and no obtruction near the container?
The container kept on the terrace of the taller building will have the highest level of water.
What is atmospheric pressure ?The level of water in a container depends on atmospheric pressure, and the atmospheric pressure decreases with height.
Atmospheric pressure, also known as air pressure, is the force exerted by the weight of air molecules in the atmosphere. It is measured in units of force per unit of area, typically in kilopascals (kPa) or pounds per square inch (psi).
Atmospheric pressure decreases with increasing altitude, as there are fewer air molecules above the earth's surface. At sea level, the average atmospheric pressure is approximately 101.3 kPa (14.7 psi), while at high elevations it can be significantly lower.
The taller building is higher up, so the atmospheric pressure on its terrace is lower than that at ground level, resulting in a lower water level in the container kept there.
The water level in the container kept on the terrace of the shorter building and the one kept in an open space will be at the same height, as they are both at ground level and have the same atmospheric pressure.
Therefore, The container kept on the terrace of the taller building will have the highest level of water.
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A semicircular loop of radius a carries positive charge Q distributed uniformly.(Figure 1) Find the electric field at the loop's center (point P in the figure). Hint: Divide the loop into charge elements dq as shown in the figure, and write dq in terms of the angle d theta, then integrate over theta. Express your answer in terms of i, j, k, Q, a.
The electric field at the center of the charged semicircular loop (point P) is given by: E = (k × Q) / (2 × a) × (i + j + k).
What is electric field?The electric field is a measure of the electric force exerted by a charged object on other charged objects in its vicinity. It is a vector quantity that specifies the direction and magnitude of the force that would be experienced by a unit positive charge placed in that field.
The electric field at the center of a charged circular loop can be calculated using the following steps:
Divide the loop into small charge elements dq, each at an angle dθ from the center of the loop (point P).
The electric field due to each small charge element dq at point P is given by:
dE = (k × dq × r) / (r²),
where k is Coulomb's constant, r is the distance from the charge element dq to point P, and r² = a² + (a × dθ)²
Integrating the above expression over the entire loop (from θ = 0 to θ = π), we get the total electric field at point P:
E = k × Q × (∫(a / (a² + (a × dθ)²) × dθ) from 0 to π)
Evaluating the above integral, we get:
E = (k × Q × a) / (2 × a) = (k × Q) / (2 × a)
Therefore, the electric field at the center of the charged semicircular loop (point P) is given by:
E = (k × Q) / (2 × a) × (i + j + k), where i, j, k are the unit vectors in the x, y, and z directions respectively.
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What is the temperature of 1000 K on the Celsius scale?
The required temperature on celsius scale when temperature on kelvin scale is given is calculated to be 726.85 °C.
The thermometer industry's two most used temperature measurement scales are the Celsius and Kelvin scales. One degree on the Celsius scale has the same value as one degree on the Kelvin scale since the temperature difference or change is the same on both measures.
The given temperature in kelvin scale is 1000K.
Let us convert it into celsius scale.
The relation between celsius scale and kelvin scale is
°C = K - 273.15
where,
°C is temperature in celsius scale
K is temperature in kelvin scale
Putting the known values into the above equation, we have,
°C = 1000 - 273.15 = 726.85 °C
Thus, the required temperature is 726.85 °C.
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two point charges of 30 μc each are 4 cm apart. what is the electric field at the midpoint between the two charges?
The electric field at the midpoint between the two charges each of 30 μC, is zero.
Charge q₁ = +30 μC
Charge q₂ = +30 μC
Distance between both the charges, d = 4 cm
Midpoint will be 2 cm from each charge. so r = 2 cm
We know the electric filed produced by a charge, at a distance of d is formulated as, E = q/(4πε₀r²)
Where q is the charge, ε₀ is the constant of permittivity of vacuum.
Let 1/(4πε₀) = k, then E = kq/r²
Electric field due to first charge at 2 cm from it, E₁ = (k × 30)/2²
Similarly, electric field due to second charge at 2 cm from it, E₂ = (k × 30)/2²
E = E₁ - E₂
E = (k × 30)/2² - (k × 30)/2²
E = 0
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Two cars leave an intersection at the same time, one heading east and the other heading south. Some time later the cars were 200 mi apart. If the car heading south travels 50 miles farther than the car going east, how far does the car heading east travel? round the answer to the nearest tenth.
If the car heading south travels 50 miles farther than the car going east, how far does the car heading east travel travels 150.0 miles, the problem can be solved by the formula d = rt.
The used equation is d = rt, The equation states that the distance traveled is equal to the rate times the time. This equation can be used to calculate the distance traveled by an object, given that the rate and time are known. In this case, the rate was the same for both cars and the time was the same for both cars, allowing us to calculate the distance traveled by a car heading east. Since we know that the car heading south traveled 50 miles farther than the car going east, we can subtract 50 miles from the total distance of 200 mi to find the distance traveled by car heading east. This gives us a value of 150 mi, which can be rounded to the nearest tenth to give us 150.0 miles.
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A satellite of mass 2,000 kg is in an elliptical orbit about the Earth: When the satellite reaches point A, which is the closest point to the Earth, its orbital radius is 1.2 x10^7 m and its orbital velocity is 7.1x 10^3 m/s. (ME = 6x10^24 kg and Re = 6.4x10^6m) - Determine the total mechanical energy of the satellite at point A assuming that the gravitational potential energy is zero at an infinite distance from the Earth.
- Determine the angular momentum of the satellite at point A.
- What is the minimum speed of the satellite at point A in order to escape from Earth?
a. The total mechanical energy is [tex]EM = -4.4*10^{14} J.[/tex]
b. The angular momentum of the satellite at point A is [tex]L = 8.5*10^{12} kg m2/s.[/tex]
c.The minimum speed of the satellite at point A in order to escape from Earth is [tex]ve = 11.2*10^{3 }m/s.[/tex]
a. The total mechanical energy of the satellite at point A is equal to the sum of its kinetic and potential energies. The kinetic energy is given by [tex]KE = \frac{1}{2} mv2,[/tex], where m is the mass of the satellite and v is the orbital velocity. The potential energy is given by [tex]PE = \frac{-GMEm}{r}[/tex], where G is the gravitational constant, M is the mass of the Earth, and r is the orbital radius. Thus, the total mechanical energy is
[tex]EM = KE + PE = \frac{1}{2} mv2, - \frac{GMEm}{r}.[/tex]. Substituting [tex]m = 2,000 kg, v = 7.1*10^{3} m/s, \\G = 6.67*10^{-11} N m2/kg2, M = 6*10^{24} kg,\\r = 1.2*10^{7} m[/tex]
we obtain[tex]EM = -4.4*10^{14} J.[/tex]
b. The angular momentum of the satellite at point A is given by L = mvr, where m, v, and r are as defined above. Substituting the given values, we obtain [tex]L = 8.5*10^{12} kg m2/s.[/tex]
c. The minimum speed of the satellite at point A in order to escape from Earth is the escape velocity, which is equal to the square root of twice the gravitational potential energy at point A. Substituting the given values for M and r, we obtain the escape velocity [tex]ve =\sqrt(2GM/r) = 11.2*10^{3 }m/s.[/tex]The minimum speed of the satellite must be greater than the escape velocity in order for it to escape from Earth.
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answer this question al six marks please my slays
Answer:
the driver need to stop before he drive
Explanation:
if he keep driving he will hit a car